Analytical and Stochastic Modelling Techniques and by Sabine Wittevrongel, Tuan Phung-Duc

By Sabine Wittevrongel, Tuan Phung-Duc

This booklet constitutes the refereed lawsuits of the twenty third overseas convention on Analytical and Stochastic Modelling innovations and functions, ASMTA 2016, held in Cardiff, united kingdom, in August 2016.

The 21 complete papers offered during this booklet have been rigorously reviewed and chosen from 30 submissions. The papers talk about the newest advancements in analytical, numerical and simulation algorithms for stochastic platforms, together with Markov approaches, queueing networks, stochastic Petri nets, strategy algebras, video game idea, etc.

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Extra info for Analytical and Stochastic Modelling Techniques and Applications: 23rd International Conference, ASMTA 2016, Cardiff, UK, August 24-26, 2016, Proceedings

Sample text

Still, there is no standard way to generate synthetic attributes for the nodes and in particular providing some level of homophily (or correlation). In the same way we can generate numerous random graphs with desired characteristics, we wanted to have mechanism to generate the values on the nodes of the given graph which will represent needed attribute, which will satisfy the following properties: 1. Nodes attributes should have the property of homophily 2. We should have the mechanism to control the level of homophily These properties are required to evaluate the performance of the subsampling methods.

Bias(ˆ μSA ) = E[ˆ (7) Then the mean squared error of the estimator, M SE(ˆ μSA ), is: μSA )2 + Var(ˆ μSA ). M SE(ˆ μSA ) = Bias(ˆ (8) This bias can be non-null if the quantity we want to estimate is correlated with the degree. In fact, we observe that the random walk visits the nodes with more connections more frequently. Subsampling has no effect on such bias, hence minimizing the variance leads to minimizing the mean squared error. 4 Matrix P ∗ is always diagonalizable for RW on undirected graph.

6) can be approximated as follows: σμ2ˆSA = Var Y¯ k = 1 m B kC1 +C2 i=2 1 + λki < g, vi >2π . 1 − λki Interestingly, the expression for the variance in the general case has the same structure as for the geometric model. Therefore, the interpretation of the formula is the same. There are two factors, that “compete” with each other. If we try to decrease the first factor, we will increase the second one and the opposite. In order to find the desired parameter k we need to find the minimum of the estimator function for variance.

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