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Einstein’s Legacy

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- Inktomi
- Never chose create its own portal
- June 2000 Stockvalue dropped by $2.8 bil
- Yahoo! Has fired
- Replaced Inktomi with google
- Almost a new comer

- Larry Page-Cofounder
- ’’ I’m feeling lucky ’’
- Addiction
- No wonder why yahoo chose google.

- Google intrigued barabasi becoz it voilated the basic prediction of Scale free model.
- First mover has the advantage.
- In SFM the most connected nodes are that appear first.
- Google launched in 1997 overtook the market with in 3 years.
- Competetors were AltaVista and Inktomi.

- Apple
- Aircraft Industry
- ’De Havilland’ – jet powered plane –Comet
- In 1949-450 miles/hr(Euro and American Mkt)
- Disasters after one year
- Chance for Boeing to take the market
- Boeing 707(5 years after Comet)-40 yrs
- The 3rd ’ The European Airbus’ entered.
- Shrinking the market of Boeing

- SFM has no such place for dominant late comers.
- They assumed that ’all nodes are identical’
- In complex networks each node has a unique characteristics.
- Some show up late and grab the market
- Some rise early yet never make it
- So if we want to calculate this competition in networks , we have to know that each node is different.

- Knack,Loyal partners & addicts(common?)
- Hard to find the universal secret, but we can point out certain char that separate the winners from losers.
- In competetion each node should has a Fitness
- Fitness is a quantitative measure of a nodes ability to stay in front of competetion

- 2 basic mechanisms governing the n/w evolution.
- Growth
- Preferential Attachment

- Fitness doesn’t eliminate these two
- But it changes in a competitive environment
- Incorporate fitness into the SFM is to assume preferencial attachment is driven by the product of nodes fitness and number of links it has

- Each node decides where to link by comparing the fitness connectivity prod.
- The probability to connect to a new node
- In SFM – k/EiKi
- The Fitness model has an additional char ’n’ – kn/EiKin.

- If Two nodes with same no of links the fittest one aqires
- If 2 nodes has the same fitness then the older one has an advantage

- Ginestra Bianconi
- Ist year graduate in Ph.d.
- Author asked her to study the properties of fitness model.
- She was born & educated in rome & she is very good at statistical mechanics
- She confirmed that in the presence of fitness the early bird is not necessaryly the winner.

- The fitness model tells nodes still aquire links following a power law
- So the speed at which nodes aquire links is nomatter of seniority
- Beauty over Age
- Dymanic Picture
- SFM – Narrow lane highway
- Fitness Model – Multilane highway

- The fitness model posed new questions
- Would the power law apply for the fitness model?
- Would networks driven by competition continue to be scale free?

BREAK

- To understand how competion shapes the networks topology our author took us back in to the time of three giants of Quantum theory
- Albert Einstein
- Max Plank
- Satyendranath bose

Eric A.Cornell

And

Carl E. weiman

In 1995 Attained the temps of Bose-einstein condensation needs.

Solved the mystery by condensing the rubidium atoms.

Nobel Prizes in after six years ie..in 2001.

From then B-E condensation became the physicists toolkit.

Bianconi reached this toolkit.

- The Mathematical transformation Biaconi sustituted for fitness of energy
E = (-1/B) log n

- So here in this mapping complex networks are like huge quantum gas , their links behave like subatomic paricles
- The prediction was – some n/w undergo Bose-Einstein Condensation
- The consequense is in some networks the winner can take all

- Fit – Get – Rich
- Despite the feirce competetion for links , the scale free topology survives

- Winner takes all
- The fittest node grabs all links
- Not a scale free network

- In reality we cannot find the second category
- Even the Google example falls under the Fit-get-rich category

- Is there any real time networks that come under the Winner takes all category?
- The answer is ’Windows’
- Gates and Allen

- As long as we thought of networks as random we modeled them as STATIC graphs
- The SFM reflects our awakening to the reality that networks are Dynamic systems that change constantly through the addition of new nodes and links.
- The fitness model allows us to describe networks as competive systems in which nodes fight fiercely for links.
- Now Bose-Einstein Condensation explains how some winners get the chance to take it all.