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This can be a standard function from a library (e.g. a scaled sum function) or an own-defined function.
By a slightly different argument a similar conclusion can be drawn when not a scaled sum combination function but a logistic combination function is chosen.
Combination functions used in this simple example are the scaled sum function and the identity function, and all connections have weight 1, except the connections to ps(_{a}), which have weight 0.5.
For well-connected temporal-causal network models based on scaled sum functions with as scaling factor the sum of the weights of the incoming connections it can be derived that all states have the same equilibrium value.
For the contagion between states, a dynamic scaled sum function has been used in which, at each point in time, the scaling factor is equal to the sum of the connection weights involved.
Let a temporal-causal network model be given based on scaled sum functions: begin{aligned} mathbf{d}Y/mathbf{d}t={upeta }_{Y} [Sigma _{X,{upomega }_{X,Y} >0} {upomega }_{X,Y }X /Sigma _{ X,{upomega }_{X,Y} >0} {upomega }_{X,Y} - Y] end{aligned}Then the following hold.
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Small β tends toward L 1 norm and large β tends like a scaled sum-of-squares measure, so different β will produce different inversion results.
The utilities are scaled to sum to zero within each factor.
The coefficients are also uniformly scaled to (sum _{t,c} r_{t,c} = C).
The coefficients are also uniformly scaled to (sum _{t,c} r_{t,c} = C). 5.
The sample weight was scaled to sum to the follow-up sample size (163).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com