Computational neuroscience: neuron and network simulation
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
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.
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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.
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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.
Navier-Stokes + Incompressible + Finite difference method
Discretization methods for approximating the Partial Differential Equations (PDEs):
Finite Difference (FD) Finite Elements (FE) Finite Volume (FV) Finite Difference (FD) Taylor’s polynomial
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Modular Arithmetic Library in C++
This library provides the basics of modular arithmetic operations:
Great Common Divisor (GCD) Least Common Multiple (LCM) Bezout solver Decomposition number algorithm Euler’s totient function Primality Test Find next Prime Inverse function Solver for 1 equation Solver for multiple equations -GitHub repository: Modular Arithmetic Source Code -Article Modular Arithmetic Article
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