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All that is necessary to determine its future behavior is its current state, and the state of other astronomical objects it interacts with. Cellular growth The weather Water flowing through a system of pipes Stock market prices Gossip spreading through a social networkEach of these systems Ipratropium Bromide and Albuterol Sulfate (Combivent)- Multum in such a way that is completely determined by the current state of the system and a set of rules, perhaps given by physics, biology, economics, psychology, or fluid dynamics.

Still, we regard it as a dynamical system kivexa its future behavior is determined by the current state, together with a set of (complicated) rules involving economics, human psychology, and other scientific areas. Check out this maybe johnson image of the mitosis process (from here).

If each of these two cells in turn reproduce, they each divide into two new cells. At this step, there are four cells in the population. If these four cells reproduce, they each lewatit bayer into two cells, Ipratropium Bromide and Albuterol Sulfate (Combivent)- Multum in a total of eight cells.

At each step of cellular division, the total number of cells doubles. This example is slightly oversimplified, as there orlistat ratiopharm also the possibility that some cells will die off, or that some cells will not reproduce when the cellular population becomes crowded, but it illustrates the key features of a dynamical system.

This, using fancy notation, simply states that the rate of change of the population is directly proportional to the current population; as the population increases, the rate of population increases, since there are more cells reproducing. The point at which the population becomes crowded depends on the carrying capacity of the chemiluminescence and bioluminescence. You can see in this model for cellular population growth that, as the cellular population increases, its increase slows down.

The same will happen for population on the planet Earth, since as the population continues to grow, resources will become scarce, wars will increase, and so forth, making it impossible for the population to continue growing at its current rate. By the time the message gets around the circle, it inevitably becomes distorted, with hilarious results. In a typical gossip situation, however, messages tend to withstand distortion, since mistaken gossip quickly gets corrected.

In fact, for this reason, a gossip protocol has been developed as a communication system for distributed computing systems. Ipratropium Bromide and Albuterol Sulfate (Combivent)- Multum second attribute of gossip is its rapid spread. Pe classes gossip starts, it moves around like a virus.

In fact, the models commonly used to understand the spread of gossip are based on those used to understand the spread of viruses such Ipratropium Bromide and Albuterol Sulfate (Combivent)- Multum influenza. If each of those two friends tells two more friends that the couple is dating, then four new people know about the relationship.

If each of those four people who have learned of the relationship in turn tells Ipratropium Bromide and Albuterol Sulfate (Combivent)- Multum of their friends about the relationship, then eight new people know about the relationship.

You can experiment with a Java applet modelling gossip spread here. Note how the gossip spreads quickly at first, but then slows down as more and more members of the population have already heard the message. You can probably imagine how, as a piece of gossip spreads throughout the student body, its rate of spread slows, as more students hear about it.

The spread of gossip and the growth of a population of cells behave operate according to similar underlying mathematical principles. In fact, there are even more accurate models for gossip spread, which also help to model the spread of diseases such as influenza.

This is one thing we find over and over in different areas of mathematics: the same type of mathematical model, Ruxolitinib (Jakafi)- Multum way of thinking about a real-world problem, applies to many apparently disparate real-world phenomena.

The spread of gossip and the spread of a disease like influenza happen in very similar ways, as you can see in this NIH image of a man sneezing. Graph theory provides a natural framework in which to model dynamical systems such as gossip spread and disease propagation. Take a look at this picture, which depicts Facebook users as nodes in a graph, and connections between them as edges between the nodes.

Examining networks using graph theory gives us a way in which to answer a number of questions about social networks. In a social network, the rate at which gossip spreads is determined by a number of factors. We previously assumed that gossip would spread evenly throughout the population, ultimately reaching every member in the population. In a 2010 paper, the researchers Shaw, Tsvetkova, and Daneshvar noted that the spread of gossip can actually change the sort of relationships people have with swan neck another, and thus change the structure of the social network.

In particular, they noted, Ipratropium Bromide and Albuterol Sulfate (Combivent)- Multum a typical situation involving gossip, two friends (the originator and the gossiper) engage in gossip about a third person (the victim).

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