Simply Complexity (17 page)

A lot of current research effort is being spent on working out exactly how humans are connected. Given that Complexity features collections of interacting objects with feedback, the nature of such connections – and in particular what information they might
carry – is clearly important. However we have to be very careful about how we define these network connections. In terms of friendship networks, for example, person A and person B may hate each other and therefore not be connected at all. However in terms of a network describing the transmission of a virus, they may well be connected if they happen to take the same bus by accident. After all, viruses don’t require that the people that they pass between actually like each other. For this reason, we will be less concerned in this book with how things are connected and more concerned with the effect of such connections. Each of the networks which we discuss is equivalent to a collection of interacting objects which are competing in some way. Hence, in addition to being networks, they are also all examples of Complex Systems.

We begin our peek at networks right down at Nature’s smallest and by far weirdest level: the nanoscale level of quantum physics. It turns out that on this scale there is an extremely important network at work – from the leaf of spinach in your salad through to the entire Amazon Rainforest. It is the network of photosynthesis – or more specifically, the network of proteins inside each leaf which carry the energy of the light arriving from the Sun to a place within the leaf where it can be converted into food for the plant. However, even though photosynthesis is one of the first things that kids are told about in Science class, it continues to throw up many surprises for scientists. In particular, recent research suggests that Nature might actually be utilizing some clever network queue-management trick, in order to control the arrival rate of the light energy to the reaction centers where the food is produced.

More generally, biological Complex Systems show a wealth of network behavior. Just as the commercial world uses transport networks to distribute goods, or the Internet to distribute information, Nature uses networks to distribute the nutrients necessary for life – from the blood-flow through veins and arteries in
our own bodies through to the nutrient-flow in forest fungi. Indeed, forest fungi represent a quite remarkable example of networks in that they consist entirely of a maze of tubes, and yet manage to stretch for miles over the forest floor – like some kind of natural “Wood Wide Web”. But what is even more remarkable is the fact that biological networks such as fungi tend to reconfigure themselves over time in response to the supply of nutrients being transported. In other words, the system’s food transport network affects its structural network and vice versa. Just imagine what would happen if we could get man-made networks to do this? We would have road networks which could rearrange themselves according to their traffic flows. This explains why scientists and engineers are so interested in understanding Nature’s networks; in addition to a general fascination about how they operate there is the hope that we can pick up a few hints about clever network designs.

The tricky thing for researchers studying the Complexity of systems such as fungi is that there is no easy way of knowing which tubes in the fungus (i.e. roads) are being used to carry food (i.e. cars) at any given time. There is no such thing as being able to view the food flow from above using a helicopter, as they do for eye-in-the-sky traffic updates. All you see from above are closed tubes, and therefore you don’t know what is flowing down what, and when. Fortunately researchers such as Mark Fricker at Oxford have managed to tag the food particles in the fungus so that they emit light – like a moving flashlight – which helps us understand where the food is flowing. But a big open question remains. How on earth do biological networks such as fungi manage to continually reroute food supplies without any centralized resource manager? This, after all, would be like Tesco or Wal-Mart never having to oversee the supply of goods to needy stores, but instead just sitting back and “letting it happen”. Researchers also want to know to what extent biological systems use or avoid potentially congested hubs – and whether this knowledge could then be used to tackle congestion in man-made networks. Likewise, an understanding of the underlying nutrient supply network could help doctors in the diagnosis and treatment of potentially lethal cancer tumors, and in treating disorders such as an AVM
(Arterio-Venous Malformation) where the brain becomes starved of nutrients as a result of short cuts in the network of vessels.

On the level of groups of humans, a particularly important network is that concerning the transmission of viruses. At the time of writing this book, bird flu looks set to invade Western Europe – and scientists fear the possibility of it combining with a more typical human flu virus, thereby creating a superbug that could be transmitted easily between humans. Just as it is important to understand the actual biology of the virus, it is also important to understand how it spreads on a network.

Our society’s safety is currently threatened by global networks of terrorism, crime and insurgency. It turns out that most modern conflicts represent a Complex System. Each is an evolving ecology with various armed insurgent groups, terrorists, paramilitaries and the army. In short, there are many interacting species which are continually taking decisions based on the previous actions of the others. In addition, these conflicts are being continually fed by an underlying supply network whose “nutrients” involve mercenaries, arms, money, drug-trafficking and kidnappings. Indeed, just as in a fungus and even a cancer tumor system, it is possible that these underlying nutrient supply chains have self-organized themselves into some reasonably robust structure, thereby making it even harder to remove or control them.

One of the most fundamental issues facing scientists is to work out the extent to which the macroscopic network structures observed in naturally occurring Complex Systems result from instructions within the genes at the microscopic cellular level. Crudely speaking, it is commonly assumed that genetics dictates structure and that structure then dictates function. But is it
really
all in our genes? This is something that David Smith, Chiu Fan Lee, Mark Fricker and Peter Darrah have been looking at very closely. They use the fungus as a particular example since they can inject tagged food into it, and thereby follow the flow of this food traffic through the fungal tubes or “roads”.

They recently found something quite remarkable. Starting with a simple biological function – namely the passing around of food – they have shown mathematically that network structures emerge which closely resemble a wide class of multi-cellular organisms such as fungi. As sketched in
figure 5.1
, the researchers’ “pass-the-food” model considers that each part of the fungus simply receives what it is passed; then it consumes what it needs to survive and passes the rest along. This is very much like a line of people passing along buckets of water on a hot day – or school-children at a traditional long school dining table, such as in the
Harry Potter
movies, passing along the serving plates of food.

In addition to generating realistic macroscopic structures, the researchers find that a wide range of important biological functions also happen to emerge from the model. These emergent properties include the abilities to store food, forage efficiently and even to physically move over large distances. Given the simplicity and generic nature of their pass-the-food rule, the researchers believe that it could play a central role in determining network structures across a wide range of natural systems. Their findings also suggest
that a fruitful method for classifying biological organisms would be by referring to what they do rather than what they look like.

Figure 5.1
Feed the fungus. The fungus transports packets of food, like traffic, along each branch in the network. The researchers’ model considers that each part of the branch simply receives what it is passed, consumes what it needs to survive, and then passes the rest along – very much like a line of people passing along buckets of water on a hot day.

There is intense commercial and academic interest in understanding the movements in the global Foreign Exchange (FX) market. It is the world’s biggest market, and the daily transactions exceed 1,000,000,000,000 US dollars in value, which in turn exceeds the yearly GDP (Gross Domestic Product) of most countries. However it is a formidable task to build such an understanding since the FX market is characterized by a complicated network of fluctuating exchange rates, with subtle interdependencies which may change in time. Indeed it is an excellent example of a real-world Complex System.

In practice, traders talk about particular currencies being “in play” during a particular period of time, as if the FX market were some type of global game as described in
chapters 1
and
4
. Until very recently, there was no established machinery for detecting such important practical information from market data. However, a joint university-commercial collaboration has recently shown that the construction of so-called Minimum Spanning Trees (MSTs) can indeed capture such important properties of the global FX dynamics. In particular Mark McDonald, Omer Suleman, and Sam Howison teamed up with Stacy Williams of HSBC Bank to uncover the network underlying the movements in the world’s currency markets. The research team then showed that this network can be used to detect which currency is “in play” among the world’s currency traders.

The novelty of their approach lies in their use of a particular type of network, called a tree, in which there are very few connections. The idea is as follows. Suppose we only have three currencies, such as the Euro, the U.S. dollar (US$) and the U.K. pound sterling (£). An exchange rate is literally an exchange of one currency for another. The shorthand A/B means the amount of currency B which one can buy with one unit of currency A, in which case A is referred to as the base currency. Likewise, it is possible to
use one unit of currency B to buy currency A – and this is represented by the shorthand B/A. This means that every pair of currencies has two exchange rates associated with it. Admittedly these rates will almost be the reverse of each other, but they are two rates nonetheless – and they will differ from each other according to whether the prevailing mood in the market favors buying currency A over B or vice versa, or selling B over A or vice versa. The example of three currencies will therefore produce six possible currency pairs – Euro/£, £/Euro, Euro/US$, US$/Euro, US$/£, £/US$. Each of these exchange rates then fluctuates in time in some complicated way. The researchers started off by drawing a network to represent the correlations between the movements of these six exchange-rates. If for example the Euro/£ rate is moving around in a similar way to the Euro/US$ rate, one would say that the two are highly correlated. If the Euro/£ rate is moving around in a way that seems unrelated to the Euro/US$ rate, one would say that the two are uncorrelated. Since there are six different exchange rates, there will therefore be ½ × 6 × 5 = 15 different correlations between pairs of exchange rates. And this is
a
lot
of information – too much, in fact, to easily digest. When scaled up to all the world’s major currencies, it would become practically impossible for traders to analyze quickly. Hence such a network of correlations in its raw form is of limited practical use.

Figure 5.2
Trees growing on money. There are three currencies: UK Sterling (£), US Dollar (US$), and the Euro. Hence there are six possible exchange rates. The appearance of a connection means that the two corresponding exchange rates are moving in a similar way – in technical terms, the two exchange rates are strongly correlated. In this example, the Euro is “in play” in the market.