## Linear Programming

Simplex Algorithm

I have coded recently the simplex algorithm. It is an algorithm that solves the optimizations of a problem of linear programming. It gives a function to minimize and constrains the variables with an inequality form. It can be proven that the simplex algorithm solves this problem in Non-Polynomial time.

## Computational Neuroscience

Computational neuroscience: neuron and network simulation

# Neuron

The neuron is the most common component in our brain,  we have nearly 86 billion neurons and 1000 trillion synaptic connections, estimates to a computer with a 1 trillion bit per seconds processor # Computational Neuroscience

Is the field of study in which we measure and simulate the neurons process. Our brain is a complex machine and its behavior is non-linear.

We need previous knowledge of electronics, ODE’s, neurobiology, chemistry, and programming.

## Lane Line Recognition

Lane line recognition algorithms

The Hough Transform has been broadly used in many fields, including autonomous cars. It is used to detect straight and curved lines with high accuracy.

This is the result of the Lane Line program I have designed to detect edges on the road.

The algorithm used, it is used to detect edges on images. Then, we discard using analytics and probability the ones which overlap each other and the less probable.

It is very efficient and can be used in parallel computing for rather good optimizations. The results are quite astonishing.

## Dynamic Systems

N-Order Linear Systems

I have done a project for my math class where we analyze the linear systems. We have classified the first and second-order linear systems and give a general formula for an n-linear system. We have used algebra notation and we have encountered with the companion matrix power to the n problem.

The n-linear systems are used widely in finance for loans, interests, etc.

GitHub repository: DynamicSystem

## Computational Fluid Dynamics (CFD)

Navier-Stokes + Incompressible + Finite difference method

Discretization methods for approximating the Partial Differential Equations (PDEs):

1. Finite Difference (FD) 2. Finite Elements (FE)
3. Finite Volume (FV)

#### Finite Difference (FD) Taylor’s polynomial   