# Development Projects

## Website for a Charity Organization

Hashimukh is a non-profit social welfare organization working solely for the betterment of underprivileged children towards a quality life. It is supported constantly by its advisory board and executive committee with guidelines, finances, encouragements, and ideas which drive the organization to better performance each day.

# Undergraduate Projects

## Machine Learning Projects

### Principal Component Analysis and Gaussian Mixture Model

This example compares different (linear) dimensionality reduction methods applied on the Digits data set. The data set contains images of digits from 0 to 9 with approximately 180 samples of each class. Each image is of dimension 8x8 = 64, and is reduced to a two-dimensional data point.

Fig: Two Principal Components of Digits Dataset

This dataset is then used as an input for the Gaussian Mixture model and clustered in 3 groups

Fig: Clustering using Gaussian Mixture Model

## ICMP Redirect Attack

An ICMP redirect message is an out-of-band message that is designed to inform a host of a more optimal route through a network, but possibly used maliciously for attacks that redirect traffic to a specific system. In this type of an attack, the hacker, posing as a router, sends an Internet Control Message Protocol (ICMP) redirect message to a host, which indicates that all future traffic must be directed to a specific system as the more optimal route for the destination. You can set up IDS to notify you when these ICMP redirect messages occur or to ignore them.

ICMP redirect packets are ignored if IPCONFIG IGNOREREDIRECT is specified in the TCP/IP profile, you are using OMPROUTE and you have IPv4 interfaces configured to OMPROUTE, or IDS policy is active for ICMP redirect attacks and the associated policy action requests that the packet be discarded.

ICMPv6 redirect packets are ignored if IPCONFIG6 IGNOREREDIRECT is specified in the TCP/IP profile, you are using OMPROUTE and you have IPv6 interfaces configured to OMPROUTE, or IDS policy is active for ICMP redirect attacks and the associated policy action requests that the packet be discarded.

By default,OS doesn’t allow ICMP redirects.In the successful attack scenario the icmp redirect bit is turned on to demonstrate the attack

Fig: Topology used

Fig: Packet Sniffing observed in Wireshark

## E-Commerce Website in Laravel: The PHP Framework

An E-Commerce Platform where customers can view different types of products. Customers can search and filter products according to different brands and categories. They can add products in their cart based on availability and complete checkout. The application is developed in PHP using Laravel framework along with MySQL.

## Invisibility Cloak using OpenCV

This project was done using an image processing technique called Color detection and segmentation. In order to do this one must have a cloth of same color and no other color should be visible into that cloth. We are taking the red cloth. If some other cloths are taken, the code will remain the same but with minute changes.

Algorithm:

Capture and store the background frame.

Detect the red colored cloth using color detection and segmentation algorithm.

Segment out the red colored cloth by generating a mask.

Generate the final augmented output to create a magical effect.

Why Red?

Colors like green or blue will also work fine with a little bit of changes in code. This technique is opposite to the Green Screening. In green screening, we remove background but here we will remove the foreground frame.

## Linear Programming in MATLAB to Solve an Optimization Problem

### Linear Programming

Linear programming. (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

### Simplex Method

Simplex method, Standard technique in linear programming for solving an optimization problem, typically one involving a function and several constraints expressed as inequalities. The inequalities define a polygonal region, and the solution is typically at one of the vertices.

## Interpolation

### Newton Interpolation

In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points.

### Spline Interpolation

In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline.

## Implementation and Comparison of Ordinary Differential Equation solving algorithms

### ODE

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable

### Algorithms Implemented

Euler

Huen

Ralston

Mid Point

Euler Method: In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method.

Huen Method: In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.

Ralston Method: Ralston's second order method is a Runge-Kutta method for approximating the solution of the initial value problem which evaluates the integrand twice for each step. Ralston's second order method is a second order procedure for which Richardson extrapolation can be used.

Midpoint Method: The midpoint method, also known as the second-order Runga-Kutta method, improves the Euler method by adding a midpoint in the step which increases the accuracy by one order.

## Approximation of Cosx Using Taylor Series

Taylor Series of cosx

Fig: Approximation of cosx using Taylor series

Fig: Error vs number of terms