Tree Inference: Response Time and Other Measures in a Binary Multinomial Processing Tree, Representation and Uniqueness of Parameters

A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc and partitioned terminal vertices. We consider an additional parameter for each arc, a measure such as time. Each vertex represents a process. An arc descending from a vertex represents selection of a process outcome. A source vertex represents processing beginning with stimulus presentation and a terminal vertex represents a response. An experimental factor selectively influences a vertex if changing the factor level changes parameter values on arcs descending from that vertex and no others. Earlier work shows that if each of two factors selectively influences a different vertex in an arbitrary MPT it is equivalent to one of two simple MPTs. Which applies depends on whether the two selectively influenced vertices are ordered by the factors or not. A special case, the Standard Binary Tree for Ordered Processes, arises if the vertices are ordered and the factor selectively influencing the first vertex changes parameter values on only two arcs. We derive necessary and sufficient conditions, testable by bootstrapping, for this case. Parameter values are not unique. We give admissible transformations for them. We calculate degrees of freedom needed for goodness of fit tests.

A Note on Hamiltonian Bypasses in Digraphs with Large Degrees

Let D be a 2-strongly connected directed graph of order p ≥ 3. Suppose that d(x) ≥ p for every vertex x ∈ V (D) \ {x0}, where x0 is a vertex of D. In this paper, we show that if D is Hamiltonian or d(x0) > 2(p − 1)/5, then D contains a Hamiltonian path, in which the initial vertex dominates the terminal vertex.

A new algorithm for the optimization of transport networks subject to constraints

Предложен эвристический алгоритм построения транспортной сети сбора оптимальной геометрии с ограничениями. Транспортная сеть представляется ориентированным взвешенным деревом Штейнера. Ограничения накладываются на максимальную суммарную длину участков коммуникаций от любой терминальной вершины до точки сбора. Учет ограничений происходит с помощью метода штрафных функций. Приведен анализ влияния параметров модели на оптимальную геометрию сети. A new heuristic algorithm of finding a minimum weighted Steiner tree is proposed. A transport network can be represented in the form of a directed weighted Steiner tree. Constraints are imposed on the maximal total length of communications from any terminal vertex to the root of the tree. A penalty function method is used to take the constraints into account. The effect of model parameters on the optimal network geometry is analyzed.