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# Education

#### ​The probability density function (PDF) of the normal distribution or Bell Curve Gaussian Distribution by Guy Lakeman

​The probability density function (PDF) of the normal distribution or Bell Curve of Normal or Gaussian Distribution is the mean or expectation of the distribution (and also its median and mode).
The parameter is its standard deviation with its variance then, A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.However, those who enjoy upskirts are called deviants and have a variable distribution :)
A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
If mu = 0 and sigma = 1
If the Higher Education Numbers Are Increased then the group decision making ability of society would be raised above that of a middle teenager as it is nowBUT Governments can control children by using bad parenting techniques, pandering to the pleasure principle, so they will make higher education more and more difficult as they are doing

85% of the population has a qualification level equal or below a 12th grader, 17 year old ... the chance of finding someone with any sense is low (~1 in 6) and the outcome of them being chosen by those who are uneducated in the policies they are to decide is even more rare !!!
Experience means little if you don't have enough brain to analyse it
Democracy is only as good as the ability of the voters to FULLY understand the implications of the policies on which they vote., both context and the various perspectives.   National voting of unqualified voters on specific policy issues is the sign of corrupt manipulation.
Democracy:  Where a group allows the decision ability of a teenager to decide on a choice of mis-representatives who are unqualified to make judgement on social policies that affect the lives of millions.The kind of children who would vote for King Kong who can hold a girl in one hand and swat fighter jets out of teh sky off the tallest building, doesn't have a brain cell or thought to call his own but has a nice smile and offers little girls sweets.

• 3 years 11 months ago

#### Prey&Predator

​Physical meaning of the equationsThe Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:
1. The prey population finds ample food at all times.2. The food supply of the predator population depends entirely on the size of the prey population.3. The rate of change of population is proportional to its size.4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.5. Predators have limitless appetite.As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.
Prey
When multiplied out, the prey equation becomesdx/dt = αx - βxy The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

• 2 years 1 month ago

#### Population Stock and Flow

This is a simple population model designed to illustrate some of the concepts of stock and flow diagrams and simulation modelling.
The birth fraction and life expectancy are variables and are set as per page 66 of the text. The population is the stock and the births and deaths are the flows.
• 4 years 6 months ago

#### Using Systems thinking for technology in education

A visual look at using technology in school based on the article:
Levin, B. B., & Schrum, L. (2013). Using systems thinking to leverage technology for school improvement: Lessons learned from award-winning secondary Schools/Districts. Journal of Research on Technology in Education, 46(1), 29-51.
• 1 year 10 months ago

#### Predator-Prey Model ("Lotka'Volterra")

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system.  The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined.  Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed.  Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:
1. The prey population finds ample food at all times.2. The food supply of the predator population depends entirely on the size of the prey population.3. The rate of change of population is proportional to its size.4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.5. Predators have limitless appetite.As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.
Prey
When multiplied out, the prey equation becomesdx/dt = αx - βxy The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

• 2 years 3 months ago

#### Information Distribution Problem

The lack of recognition of efforts is a plague of society, an immense amount of effort goes unrecognized. Meaning there is constant input on behalf of an individual with a varying degree of output. This is a highly concerning situation for the system as a whole. For a positive feedback loop to take place, inputs must balance with outputs, respectively.
In this model, inputs balance with outputs creating a dynamic contribution.

• 1 month 3 weeks ago

#### Student Achievement

In this model I am trying to depict the multiple factors and interactions that impact student academic achievement.  As educators, our goal is to optimize the progression of academic achievement, or as represented in this stock flow diagram maintain the stock (academic achievement) at the highest level.  Multiple factors enhance achievement and, conversely, multiple factors interact to reduce the stock/rate of achievement.  As individual teachers, we must understand the factors and relationships that increase and decrease achievement.  In particular, teachers in training need to begin to build a mental model of these factors and relationships.  Only then can we optimize our individual learning environments to ensure each child reaches his/her academic achievement potential.
• 7 years 1 month ago

#### BridgingTheGap

From HBR study, 2014; combined with Solow Growth Model, explains why business seeks technological solutions.  Yet this is not sustainable, as there is a limit to the number of STEM-trained individuals to create technological solutions.
• 4 years 4 months ago

#### Fourier series

A Fourier series is a way to expand a periodic function in terms of sines and cosines. The Fourier series is named after Joseph Fourier, who introduced the series as he solved for a mathematical way to describe how heat transfers in a metal plate.

The GIFs above show the 8-term Fourier series approximations of the square wave and the sawtooth wave.

• 2 years 6 months ago

#### Launched at an Angle

object is projected with an initial velocity u at an angle to the horizontal direction.

We assume that there is no air resistance .Also since the body first goes up and then comes down after reaching the highest point , we will use the Cartesian convention for signs of different physical quantities. The acceleration due to gravity 'g' will be negative as it acts downwards.

h=v_ox*t-g*t^2/2
l=v_oy*t
• 2 years 6 months ago

#### Bio103 Predator-Prey Model ("Lotka'Volterra")

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system.  The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined.  Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed.  Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:
1. The prey population finds ample food at all times.2. The food supply of the predator population depends entirely on the size of the prey population.3. The rate of change of population is proportional to its size.4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.5. Predators have limitless appetite.As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.
Prey
When multiplied out, the prey equation becomesdx/dt = αx - βxy The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

• 8 months 17 hours ago