Additive-ratio measures of interactivity in input-output systems

Article Abstract:

A class of additive-ratio (AR) measures was examined within an axiomatic framework developed for the measurement of alternative interactivity levels within a given activity system. Results revealed that AR measures can be described by specific axioms of interactivity, namely, the similarity, symmetry, independence and reducibility axioms. Alternative measures of interactivity were also developed and compared to AR measures within the context of these four axioms and the conditions of continuity, minimality and monotonicity.

Econometrics, Axioms

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Gravity-type interactive Markov models - part I: a programming formulation of steady states

Article Abstract:

A gravity-type interactive Markov migration model was utilized in relaton to the study of collective population's migration behavior. Utilization of gravity-type model revealed that a flow version of the steady-state problem can be addressed with a programming formulation that allows global assessment of steady-state behavior. Steady states become unique in situations where attractiveness is lessened by an intensifying population congestion.

Population transfers

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Gravity-type interactive Markov models - Part II: Lyapunov stability of steady states

Article Abstract:

A programming formulation used in gravity-type interactive Markov models were utilized to assess the stability of interactive Markov chains. The programming formulation forms a Lyapunov function for the continuous-time version of spatial-flow chains. It is shown that the stability of continuous-time versions of interactive Markov chains is highly dependent on the Lyapunov stability properties of spatial-flow chains.

Liapunov functions

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