The optimal path of the tumor particle must be instantaneously normal to an arbitrary curve in the circular cross-section.

<p>The optimal path of the tumor particle must be instantaneously normal to an arbitrary curve in the circular cross-section.</p

An image of the vector field of a portal vein.

<p>The arrows represent the various energy transfer pathways. The curve represents a “contour” that passes through all of the arrows at the same time, where time is projected onto the model as the fourth dimension.</p

Degree distribution of our user network, , , .

<p>User nodes have a power-law degree distribution with the power exponent .</p

Cumulative distribution of the number of participants for each topic cluster in Tianya BBS.

<p>About 90 percent of clusters attract more than 10 participants, indicating some of the least popular topics can still have some followers. Meanwhile, when is large, the probability curve decreases significantly with the increase of , and only a tiny fraction of topics attract several thousand users. The intermediate quantity occupies at least 80 percent of topic clusters, implying is the common pattern of participants in a topic cluster.</p

Distribution of waiting time between consecutive threads published by a typically selected user after 5000 time steps, , , .

<p>The distribution of the time differences between consecutive threads published by a typically selected user is approximated by where , indicating that a user activity pattern has non-Poisson statistics.</p

Number of posts varying their number of replies after 200 time steps, , , and .

<p>This distribution decays as a power law along with a long tail. The power exponent is .</p

Total number of replies for each user as a function of the number of user's topic interest.

<p>Some users that are interested in many topics usually create several replies for each topic and never join in further discussions. On the contrary, some users concentrating on only a few topics might debate with others and publish many replies to support their own opinions. The most active user that publishes about 1500 replies is only interested in 6 topics.</p

Distribution of the number of users' topic interests in Tianya BBS.

<p>The double logarithmic curve shows a power-law property, with the power exponent of . Most users concentrate on less than 10 topics, and none of users have more than 200 topic interests.</p

Cumulative distribution of the number of participants for each cluster after 200 time steps, , , and .

<p>This curve decays more and more rapidly in the double logarithmic coordinates. This distribution coincides with the Tianya BBS in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050912#pone-0050912-g002" target="_blank">Fig. 2</a>.</p

Gini coefficient for the distribution of participants in each topic cluster and in each post as a function of time in Tianya BBS.

<p>The two Gini coefficients increase quickly in the early stage. However, the Gini coefficient for posts' participants eventually tends to become relatively stable, while the Gini coefficient for clusters' participants may decrease markedly.</p