"A self-organizing system not only regulates or adapts its behavior, it creates its own organization. In that respect it differs fundamentally from our present systems, which are created by their designer. We define organization as structure with function. Structure means that the components of a system are arranged in a particular order. It requires both connections, that integrate the parts into a whole, and separations that differentiate subsystems, so as to avoid interference. Function means that this structure fulfils a purpose." (Francis Heylighen & Carlos Gershenson, "The Meaning of Self-organization in Computing", IEEE Intelligent Systems, 2003)
"At an anatomical level - the level of pure, abstract connectivity - we seem to have stumbled upon a universal pattern of complexity. Disparate networks show the same three tendencies: short chains, high clustering, and scale-free link distributions. The coincidences are eerie, and baffling to interpret." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)
"Average path length reflects the global structure; it depends on the way the entire network is connected, and cannot be inferred from any local measurement. Clustering reflects the local structure; it depends only on the interconnectedness of a typical neighborhood, the inbreeding among nodes tied to a common center. Roughly speaking, path length measures how big the network is. Clustering measures how incestuous it is." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)
"By its very nature, the mathematical study of networks transcends the usual boundaries between disciplines. Network theory is concerned with the relationships between individuals, the patterns of interactions. The precise nature of the individuals is downplayed, or even suppressed, in hopes of uncovering deeper laws. A network theorist will look at any system of interlinked components and see an abstract pattern of dots connected by lines. It's the pattern that matters, the architecture of relationships, not the identities of the dots themselves. Viewed from these lofty heights, many networks, seemingly unrelated, begin to look the same." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)
"By 'network' I mean a set of dynamical systems that are 'coupled together', with some influencing the behavior of others. The systems themselves are the nodes of the network- think of them as blobs - and two nodes are joined by an arrow if one of them (at the tail end) influences the other (at the head end). For example, each node might be a nerve cell in some organism, and the arrows might be connections along which signals pass from one cell to another." (Ian Stewart, "Letters to a Young Mathematician", 2006)
"Connectivity harbors other risks too. As we create more links among the nodes of our technological and social networks, these networks sometimes developed unexpected patterns of connections that make breakdown more likely. They can, for instance, develop harmful feedback loops - what people commonly call vicious circles - that reinforce instabilities and even lead to collapse." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)
"Initially, increasing connectedness and diversity helps, but as the connections become increasingly dense, the system gets very strongly coupled so that a failure in one part reverberates throughout the entire network." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)
"Nodes and connectors comprise the structure of a network. In contrast, an ecology is a living organism. It influences the formation of the network itself." (George Siemens, "Knowing Knowledge", 2006)
"Scale-free networks are particularly vulnerable to intentional attack: if someone wants to wreck the whole network, he simply needs to identify and destroy some of its hubs. And here we see how our world’s increasing connectivity really matters. Scientists have found that as a scale-free network like the Internet or our food-distribution system grows- as it adds more nodes - the new nodes tend to hook up with already highly connected hubs." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)
"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)
"Networks may also be important in terms of view. Many models assume that agents are bunched together on the head of a pin, whereas the reality is that most agents exist within a topology of connections to other agents, and such connections may have an important influence on behavior. […] Models that ignore networks, that is, that assume all activity takes place on the head of a pin, can easily suppress some of the most interesting aspects of the world around us. In a pinhead world, there is no segregation, and majority rule leads to complete conformity - outcomes that, while easy to derive, are of little use." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)
"A graph enables us to visualize a relation over a set, which makes the characteristics of relations such as transitivity and symmetry easier to understand. […] Notions such as paths and cycles are key to understanding the more complex and powerful concepts of graph theory. There are many degrees of connectedness that apply to a graph; understanding these types of connectedness enables the engineer to understand the basic properties that can be defined for the graph representing some aspect of his or her system. The concepts of adjacency and reachability are the first steps to understanding the ability of an allocated architecture of a system to execute properly." (Dennis M Buede, "The Engineering Design of Systems: Models and methods", 2009)
"Complexity theory embraces things that are complicated, involve many elements and many interactions, are not deterministic, and are given to unexpected outcomes. […] A fundamental aspect of complexity theory is the overall or aggregate behavior of a large number of items, parts, or units that are entangled, connected, or networked together. […] In contrast to classical scientific methods that directly link theory and outcome, complexity theory does not typically provide simple cause-and-effect explanations." (Robert E Gunther et al, "The Network Challenge: Strategy, Profit, and Risk in an Interlinked World", 2009)
"The simplest basic architecture of an artificial neural network is composed of three layers of neurons - input, output, and intermediary (historically called perceptron). When the input layer is stimulated, each node responds in a particular way by sending information to the intermediary level nodes, which in turn distribute it to the output layer nodes and thereby generate a response. The key to artificial neural networks is in the ways that the nodes are connected and how each node reacts to the stimuli coming from the nodes it is connected to. Just as with the architecture of the brain, the nodes allow information to pass only if a specific stimulus threshold is passed. This threshold is governed by a mathematical equation that can take different forms. The response depends on the sum of the stimuli coming from the input node connections and is 'all or nothing'." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
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