Courses/Computer Science/CPSC 203/CPSC 203 Template/Lecture Template/Lecture 2
Contents
Housekeeping
Required Reading
This lecture is based on the Scientific American Article, Scale Free Networks : http://www.nd.edu/~networks/Publication%20Categories/01%20Review%20Articles/ScaleFree_Scientific%20Ameri%20288,%2060-69%20(2003).pdf
See also TEXT READINGS at bottom of Wiki for some readings that will round out this discussion.
Introduction
In the last lecture, we introduced a pair of concepts for problem solving: Algorithm (a mechanical process for solving a problem) and Heuristic (a rule of thumb for solving a problem). And looked at various examples where these concepts might apply.
Today we introduce a second pair of principles: working hypothesis and error in the context of a brief history of the Internet, and our evolving understanding of it's structure and dynamics.
At the end of this lecture you should:
- have an intitial understanding of the role of "working hypothesis" and "error" in problem solving.
- be introduced to some very basic Internet-centric vocabulary
- understand the notion of a Scale Free network, it's structure, and dynamics.
Glossary
- Hub - A node with many edges. In terms of web pages, a hub is considered a web page that is linked to by many other web pages.
- TCP/IP (Transfer Control Protocol/Internet Protocol) -
- Email - A system for sending and receiving messages electronically over a computer network, as between personal computers.
- HTTP (Hyper Text Transfer Protocol) -
- WWW (World Wide Web) -
- HTML (Hyper Text Mark-up Language) -
- XML (eXtensible Markup Language) - File type.
- Web 1.0 - A general reference to the World Wide Web during its first few years of operation. The term is mostly used to contrast the earlier days of the Web before blogs, wikis, social networking sites and Web-based applications became commonplace.
- Web 2.0 - An umbrella term for the second wave of the World Wide Web, which was coined by O'Reilly Media (www.oreilly.com) and CMP Media (www.cmp.com) in their 2004 and subsequent conferences on the subject. Sometimes called the "New Internet," Web 2.0 is not a specific technology; rather, it refers to two major paradigm shifts. The one most often touted is "user-generated content," which relates more to individuals. The second, which is equally significant, but more related to business, is "thin client computing."
- Scale-Free Network - A scale-free network is a noteworthy kind of complex network because many "real-world networks" fall into this category. In a scale-free network there are some highly connected nodes, the "hubs" that connect to many other sites. Scale free networks are resistant to random attacks but direct attacks on the hubs are more volatile and can lead to failure. See detailed notes below.
Concepts
The concepts covered in this lecture include:
- Working Hypothesis and Error
- Brief History of the Internet
- Scale Free Networks
(Working) Hypothesis and Error
"All observation is for or against some hypothesis" -- Darwin.
" Hypothesis non fingo" (I posit no hypothesis) -- Newton
Hypothesis: A suggested explanation for a phenomenon; a provisional idea whose merit requires evaluation.
Error: literally, "wandering or "straying". The basic notion is that there is some true value X, and their is another value x that may come from a model, hypothesis, a guess. The difference between these values, |X-x| is the error.
assertion: It is the interplay of Hypothesis and Error that leads to increases in knowledge.
Brief History of the Internet
In the history of the Internet the actual Structure and Dynamics of the Internet went through a series of hypotheses that had to be refined, as our model's of the Internet's structure were often found to be in error with the actual structure observed.
- Cartoon history of the Internet (Arpnet(TCP/IP) -- Internet(Email was the "killer" app) --- Web 1.0(HTTP and HTML) ---- Web 2.0 (XMLs)
- Some Critical People
- Vint Cerf -- Developed TCP/IP that led to Arpnet
- Ray Tomlinson -- Developed first email system
- Tim Berners Lee (TBL) -- Developed HTML and HTTP protocols leading to world-wide web
- W3C led by TBL -- Develops XML standards, Ontology Protocols, and other protocols leading to "Semantic Web"
Scale Free Networks
- The notion of a scale free network -- follows a Power Law (see below) and has the unique property that the same pattern occurs at all network scales.
- How a scale free network develops (growth, and preferential attachement of new nodes to existing nodes with higher connectedness)
- Properties of scale free networks as they relate to the Internet (resistant to random attacks, theoretically vulnerable to directed attacks on hubs, in a scale free network there is no minimum threshold for viral contagion).
Scale Free Properties I: Dynamics
- The following are excerpts from Scale-Free Networks by Barabasi and Bonabeau (see resources)
- When deciding where to establish a link, a new node prefers to attach to an existing node that already may have other connections. These two basic mechanisms - 'growth and preferential attachement - will eventually lead to the system's being dominated by hubs, nodes having an enormous number of links.
- A growing network with preferential attachment will indeed become scale-free, with its distribution of nodes following a power law.
- The mechanism of preferential attachment tends to be linear (a new node is twice as likely to link to an existing node that has twice as many connections as its neighbors).
- If a new node is four times as likely to link to an existing node that has twice as many connections, one hub will tend to run away with the lion's share of connections. In such "winner take all" scenarios, the network eventually assumes a star topology with central hub.
Scale Free Properties II: Structure
- "Small Worlds" Phenomena -- small characteristic path length between two random nodes.
- Resistant to Random Attacks
- Susceptible to Directed Attacks on Hubs (theoretically)
- No minimal viral threshold -- viruses can 'hang around' and reinfect population
Scale Free Networks and Power Laws
- Scale Free Networks are Examples of Power Laws
- Power laws are of the form: P(K) ~ 1/K ** B -- Yikes, MATH! What does this mean?
- It means: P(K) is the Probability that a node in the network, connects with K other nodes. The coefficient "B" varies between 2-3 for most real networks.
- Other Examples of scaling:
- Plant Productivity/ Area
- Bone length and cross-sectional area
- The above are examples of "Allometric Relationships" where two attributes of an organism maintain a power-law relationship. See : http://en.wikipedia.org/wiki/Allometric_law
- Fractal Branching. E.g. for the May Equation (also called the "Logistic Map"): Xt+1 = rxt(1-xt)
- For more on the May Equation/ Logistic Map see: http://en.wikipedia.org/wiki/Logistic_map
- For more on scaling as it applies to equations similar to the Logistic Map see: http://en.wikipedia.org/wiki/Feigenbaum_function (warning -- this reference is more "math technical" -- just note the function is in the form of a (complicated) power law.
Summary
- In the history of the Internet, working hypotheses about it's structure, and even it's rationale have been modified as errors were identified through observation (or through creation).
- Scale Free Networks are the current Hypothesis about the Structure and Dyamics of the Internet, positing that,
- Dynamics of the Internet are governed by (a) growth and (b) preferential attachment.
- Structure of the Internet have several key attributes, (a) Small Worlds phenomena, (b) reistance to random attacks, (c) susceptible to direct attacks on hubs and (d) no minimal viarl threshold.
As we continue to study the Internet, it is likely that our hypotheses will continue to be updated as errors are discovered between "what we expect" and "what we find". As an example, there have been some recent critiques of the Scale Free Network concept. The philosopher/scientist Evelyn Fox Keller, has a particularly good non-technical article critiquing the current paradigm around Scale Free Networks:
see -- http://www.hot.caltech.edu/bast/KellerBioEssays.pdf
Text Readings
These text readings will round out the material in this lecture with some additional background information on the Internet, World Wide Web, and Tim Berners-Lee, creator of the World Wide Web.
- Chapter 3: The World Wide Web, Fluency with Information Technology - Skills, Concepts, and Capabilities 3rd Edition, p. 78 - 80
- Chapter 3: The Internet and the Web, Fluency with Information Technology - Skills, Concepts, and Capabilities 3rd Edition, p. 80 - 82
- interview Tim Berners-Lee, Fluency with Information Technology - Skills, Concepts, and Capabilities 3rd Edition, p. 692 - 693
Resources
- See http://en.wikipedia.org/wiki/Scale-free_network
- and particularly the wonderful Scientific American Article, "Scale-Free Networks": http://www.nd.edu/~networks/Publication%20Categories/01%20Review%20Articles/ScaleFree_Scientific%20Ameri%20288,%2060-69%20(2003).pdf
- but compare the article above's views, to the more cautionary tale found in, "Revisitng 'scale-free' Networks":
http://www.hot.caltech.edu/bast/KellerBioEssays.pdf
- One of the "pioneers" in exploring the Internet as if it were an ecosystem is Bernardo Huberman. Here is a link to his book, "The Laws of the Web" and other research: http://www.hpl.hp.com/research/idl/people/huberman/
- The Laws of the Web. Patterns in the Ecology of Information. 2001. By B.A. Huberman.
- Linked. How Everything is Connected To Everythiung Else and What it Means for Business, Science, and Everyday Life. 2003. By AL Barabasi.
- Weaving the Web. The Original Design and Ultimate Desitny of the World Wide Web by its Inventor. 1999. Tim Berners-Lee.
- Chapter 16: The World Wide Web, Computer Science Illuminated 3rd Edition, p. 505 - 528
Homework
(none)
