Einstein s legacy
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Einstein’s Legacy. Introduction. 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. Google. Larry Page-Cofounder ’’ I’m feeling lucky ’’ Addiction No wonder why yahoo chose google. 1.

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Introduction
Introduction

  • 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


Google
Google

  • Larry Page-Cofounder

  • ’’ I’m feeling lucky ’’

  • Addiction

  • No wonder why yahoo chose google.


Einstein s legacy
1

  • 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.


History of bussiness
History of bussiness

  • 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


Einstein s legacy

  • 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.


Einstein s legacy
2

  • 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


Einstein s legacy

  • 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


Einstein s legacy

  • 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


Einstein s legacy
3 connectivity prod.

  • 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.


Einstein s legacy


Einstein s legacy

BREAK


The three giants
The Three Giants power law

  • 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


Einstein s legacy

Eric A.Cornell power law

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.


Einstein s legacy

  • 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


Two categories
Two Categories fitness of energy

  • 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


Einstein s legacy


Wraping up conclusion
Wraping Up / Conclusion takes all category?

  • 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.