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As an example of a problem described by a marked point process the dynamic response of a bridge to a random train of moving loads with random weights and speeds is treated.
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By virtue of the Marking theorem [17], the resulting process corresponds to a marked point process (MPP) on the product space R 2 × R + with intensity λ f X (x) [17].
Thus, the data represented a typical example of a marked point pattern.
To model quantitative genomic data, we consider a marked point process.
It is proposed to recognize uncertainty in the spatial positions of the clients, and possible spatial autocorrelation as well, by considering the random inputs of the optimization as one realization of a spatial marked point process.
For instance, one group of curves, the conchoids (from the Greek word for "shell"), are formed by marking off a certain length on a ruler and then pivoting it about a fixed point in such a way that one of the marked points stays on a given line; the other marked point traces out a conchoid (see the figure).
Then, the intercapillary distances are manually measured by using the marked points.
For this purpose, we simulate the marked point processes by using the birth-and-death dynamics, which simulates a Markov chain with only the birth transition adding a point to the configuration and the death transition removing a point from the configuration and holds the detailed balance condition in the continuous space (Descombes et al., 2009).
In the four titrations just mentioned, except coulometric titrations, the end point is indicated by a marked change in the electrical quantity that is being measured.
These form a marked spatial point process that we analyzed using standard spatial statistics [12].
Use a 0.04 inch (1 mm) ball bur to indent the marked point.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com