Model thinking

Standard deviation 

The standard deviation equals 12(√N)

Variation

1. Calculate the average value
2. Subtract the value less the avarage
3. Add the step 2) per value

Variation per category

1. Calculate the average value
2. Calculate the variation per category
3. Divide the category variation between the global variation from step 1).

Big Coefficient Vs New Reality

Implementation of a standardization also create a New Reality

Fashion

The velocity of how a fashion can be spread  is based in the threshold of each person to adapt the new fashion.

Prisoner Dilema

A person have more wiliness to cooperate as the opportunities of interaction decrease, so a relationship is builded according with the planned period to convey

Innovation

Innovation is the key factor to continue having a growth in a economy

Contagion Model

N= All population 

Wt = Infected People

C = Contact Rate

T = # Meetings
a = Cured People

Probability     

Wt+1 = Wt + [ NCT *  (Wt / N) (N - Wt / N)  ]

Probability of contagious = W (W - N)

SIS Model
Wt+1 = Wt + [ NCT *  (Wt / N) (N - Wt / N)  ] - aWt
          = Wt + Wt [ CT * (N-Wt / N) - a ]

Basic Reproduction Number: Tell if something is going to spread
Ro = CT/a

If Ro > 1 then spread

People need to be vaccinated (V)
V = 1 - 1/Ro

Diversity Index

Probability of fall in a tipping point

1. First square all the probabilities
2. Sum the probabilities
3. Take the inverse = 1/Sum of square probabilities

Mt Fuji Landscape

If do a graph of all the solutions for a problem, going to appear a Fuji Landscape with the optimal solution at the peak.

No Free Lunch

1. All algorithms that search the same number of points with the goal of locating the maximum value of a function defined on a finite set perform exactly the same when averaged over all possible function
2. Unless you know something about the problem being solved, no algorithm or heuristic perform better than any other.

Combinations

Calculate the number of combinations =  T * T-1 * T-2 / 3 * 2 * 1

T = Total of elements

Markov Process

_______________________            _________________
| Group 1         | % To Group 1 |       | Probability of group 1 |
________________________        __________________
|% To Group 2 |   Group 2        |       | Probability of group 2 |
________________________         _________________

Lyaponuv Function

This theorem establish a movement continue until find a top or bottom that stop it.

Always have a minimum and maximum 

Polya Process

All portfolio's projects are dependent among them

Networks

Average degree =  (2*edges) / nodes

Average path = sum of all path lengths / total combination paths

Number of possible triangles = # nodes * (# nodes - 1)  * (# nodes -2) / 3 * 2 * 1

Cluster coeficient = 1/ # of triangles

Connected Network: A network is connected if P > 1 / (N-1)

Skill Vs Luck

Paradox of Skill:  when the difference in skill between groups or individuals is very small, the winner is often determined by luck.

Relationship between skill & luck = [p * Luck] + [(1-p) * Skill] 

Having more fronts rise the possibilities of win

Cooperation

Way to cooperate are:

1. Repeated
2. Reputation 
3. Network Reciprocity
4. Group Selection
5. Kin Selection
6. Laws
7. Incentives

Projects

The people only contribute with the difference between the project cost minus the sum of the rest of participants efforts.

Never contribute with all that each can.

Calculate the value to do something 

M = Value to pay

c = cost of effort

p = probability of not work and still get a benefit 

M >= c / (1-p)

Replicator Equation

The probability of use a payoff

P1 = (Payoff * Probability) / Sum of (Payoff * Probability)

Fisher's Theorem

Higher variance increases rate of adaptation

Linear Models

Categories reduce the Variation

Diversity Prediction Theorem

Crowd Error = Average Error - Diversity
To calculate the error I need to know the result value

N