ATTITUDE CHANGE, AFFECT CONTROL, AND EXPECTATION STATES IN by Noah E. Friedkin and Eugene C. Johnsen

By Noah E. Friedkin and Eugene C. Johnsen

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Extra resources for ATTITUDE CHANGE, AFFECT CONTROL, AND EXPECTATION STATES IN THE FORMATION OF INFLUENCE NETWORKS

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1 Introduction To our knowledge, the conventional gradient or gradient-based neural networks (GNN) could be viewed as a useful and important method for time-invariant problems solving [1,2]. However, many time-varying problems intrinsically exist in mathematics, science and engineering areas [2,3,4,5,6], such as the timevarying matrix square roots (TVMSR) problem depicted as below: X 2 (t) − A(t) = 0, t ∈ [0, +∞), (1) where, being a smoothly time-varying positive-definite matrix, A(t) ∈ Rn×n and ˙ its time derivative A(t) are both assumed known numerically (or at least measurable accurately).

Overall GNN Simulink model applied to time-varying square roots solving 5) The MATLAB Fcn block can be used to generate matrix A(t) with the Clock block’s output as its input or can be used to compute the matrix norm. 6) The Math Function block can perform various common mathematical operations, and, in our context, generates the transpose of a matrix and so on. 7) The To Workspace block, with its option “Save format” set to be “Array”, is used to save the modeling results and data to the workspace.

6 0 20 40 60 80 100 120 140 Time (Hours) Fig. 4. Comparison of tidal current for 69# Table 1. 4 Table 2. Values for phase (º)of control nodes along open boundary Tidal constituents M2 K1 Qinghuang dao -140 -155 -170 120 135 150 Changxing dao 50 65 80 30 45 60 Tidal constituents S2 O1 Qinghuang dao -60 -75 -89 10 25 40 Changxing dao 100 115 130 55 70 85 An interesting phenomenon is founded by analyzing the result of designed cases, that is the tidal amplitude is not affected by the change of tidal phase in its assumed range.

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